A phase-field framework for brittle fracture in quasi-crystals

Abstract

Most of quasi-crystals are brittle at room temperature due to their specific cluster structures. Phase-field fracture models have demonstrated a powerful ability to predict brittle crack evolution. This paper develops a phase-field framework for modeling macroscopic brittle fracture in quasi-crystal solids. The kind of quasi-crystals is not preset in the phase-field model; therefore, this model is valid for almost all quasi-crystal solids. The phase-field model for the first time introduces a volume fraction parameter into the fracture toughness to reflect the effect of phason wall. Furthermore, a new numerical implementation approach of phase-field fracture models in Comsol Multiphysics is presented. Several examples of 1D hexagonal and 2D decagonal quasi-crystals are performed. The developed model is validated against the reported results of benchmark problems. Further investigations indicate that the phason field peculiar to quasi-crystals has a certain influence on the crack paths in asymmetric fracture problems and on the force–displacement curves in both symmetric and asymmetric fracture problems. When the fracture toughness is fixed, the increase of the volume fraction parameter results in the decrease of the peak force and the increase of the failure displacement. When the influence of the phason field on the fracture toughness is considered, both the peak force and failure displacement would sharply decrease, which indicates that the degradation of fracture toughness due to the phason field plays a more important role than the phason elastic energy in the fracture of quasi-crystals. Furthermore, the relation between the phonon-phason energy transformation and the elastic constants of QCs has been qualitatively analyzed. The developed phase-field modeling framework provides a guidance for understanding the fracture mechanism of quasi-crystals and assessing the safety of quasi-crystal structures in engineering practice.